I. Introduction
The asynchronous counter shown in Fig. 1 is one of the simplest but essential building blocks in very large scale integration design [1], [2]. It has been used for a long time in almost all electronic systems, including microprocessors, memories, communication devices, scientific instrumentation, and measurement systems [3]. for speeding up the counting operation of synchronous counters, a high-speed carry propagation circuit, such as a Manchester carry chain, has been used. Unfortunately, however, the operation of conventional synchronous counters is known to be very inefficient as far as the switching power consumption is concerned, since they have a lot of redundant transitions on internal switching nodes during counting operations [4], [5].